Multilevel analysis for ordinal responses

[shkingdom]

Dear all,

I need to fit a multielvel model for an ordinal response. Does Stata or MLwiN have a command for conducting a multilevel ordinal logistic regression when the model violates the parallel regression or proportional odds assumption? Many readings state that it is important to checek the assumption but they do not spell out how to resolve the problem except for fitting the multinomial model. Additionally, are there any tests to check the parallel regression assumption for the multilevel ordered model?

Thanks in advance,

Wander

[GeorgeLeckie]

Hi Wander,

Yes, you can use fit multilevel ordinal logistic models in MLwiN and allow the effects of covariates to vary across the log-odds contrasts, thus relaxing the proportional odds assumption.

See Chapter 11 of the MLwiN User Manual
http://www.bristol.ac.uk/cmm/software/m ... al-web.pdf
http://www.bristol.ac.uk/cmm/media/runm ... e_Model.do

You can fit multilevel ordinal logistic models in Stata 13 using -meologit-, but I don't believe you can relax the proportional odds assumption.

Best wishes

George

[shkingdom]

Hi George,

Thanks for your answer. I've looked at the manaul (Chapter 11). What I understand from the reading is that if the model violates the proportional odds assumption, we should consider other models such as the multilevel multinomial model which can be fitted in Stata. I guess there is no stereotype or generalized ordered logit model to the multilevel model?
Is ther any formal test to check whether the model violates the proportional odds assumption? If I'm correct, what the manual does to check the assumption is to descriptively inspect the cofficient of a variable.

Thank you,

Wander

[GeorgeLeckie]

Hi Wander,

What you can do is partially relax the proportional odds assumptions by allowing the effects of subsets of the covariates to vary across the log-odds contrasts. You can test the proportional odds assumption for a particular covariate by performing a Wald test that the effects of a covariate across the different log-odds equations are the same. Multinomial logit typically enforces the effects of all of the covariates to vary across the log-odds contrasts.

Yes you can fit a multilevel multinomial response models in Stata, but you will have to formulate them as multilevel structural equation models using the -gsem- command.

Best wishes

George

[shkingdom]

Thanks George,

Since I'm new to MlWin and runmlwin, would you refer me to the syntax or readings to learn how to test the assumption? I guess it's also possible to apply sampling weights to the analysis and test.
Thanks,

Wander

[GeorgeLeckie]

Hi Wander,

MLwiN offers two estimation methods for discrete response models: quasilikelihood and MCMC. The latter is preferable as it does not suffer from the biases which can arrise when applying the former. The magnitude of these biases can often be small, but not always. Typically, the more clustering in the data the worse the biases. Unfortunately, you can only specify sampling weights using the quasilikelihood methods.

George

[GeorgeLeckie]

Hi Wander,

In terms of testing the proportional odds assumption, just use Stata's -test- command in the usual way to test the null that the set of coefficients for a covariate are equal across the different log-odds contrasts.

Best wishes

George